CHAP. III.] BASE BY SOUND " 75 



is not so great as the retardation caused in the opposite direc- 

 tion, as in the latter case the disturbing cause has clearly acted 

 for a longer period. The formula used is — 



T 



t + t 



when T is the mean interval required, 

 t the interval observed one way, 

 t ^ the interval the other way. 



The mean interval thus found, multiplied into the velocity 

 of sound for the temperature at the time, will give the required 

 distance. 



The velocity of sound varies considerably, and an accurate Velocity 

 law for all its causes of variation has not yet been discovered. 

 The main cause is, however, temperature, and for this it can, 

 to a certain extent, be corrected. 



The most trustworthy experiments made show that sound 

 travels about 1,090 feet in a second of time, at the temperature 

 of 32° Fahrenheit, and increases at the rate of 1-15 foot for each 

 degree of temperature above the freezing-point, decreasing in 

 the same proportions for temperatures lower than 32°. 



This is the only correction that can be made, and a base 

 measured in the manner described, with these data, will give 

 an approximation sufficiently near for all practical purposes. 



As an example, let us suppose A and B the two ends of the J^^I^^P^® 

 base to be measured. Sound. 



At A have been observed 



44 beats with watch beating 5 beats to 2 seconds. 



45 



44 



Mean 44-33 beats = 17-732 seconds. 



81 beats with watch beating 9 beats to 2 seconds 



82 



83 



Mean 82 beats = 18-204 seconds. 

 Mean at A= 17-968 seconds. 



* See Appendix F. 



